標(biāo)題: Titlebook: Value Functions on Simple Algebras, and Associated Graded Rings; Jean-Pierre Tignol,Adrian R. Wadsworth Book 2015 Springer International P [打印本頁] 作者: 調(diào)停 時間: 2025-3-21 19:50
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書目名稱Value Functions on Simple Algebras, and Associated Graded Rings讀者反饋學(xué)科排名
作者: 漸強 時間: 2025-3-21 22:16 作者: 誘騙 時間: 2025-3-22 02:52 作者: Gullible 時間: 2025-3-22 06:28
Graded and Valued Field Extensions,sion of graded fields. Henselian fields are shown to satisfy a tame lifting property from graded field extensions, generalizing the inertial lifting property. In §., we lay the groundwork for the subsequent developments by an independent study of graded fields, their algebraic extensions and their Galois theory.作者: Arb853 時間: 2025-3-22 09:51 作者: ANN 時間: 2025-3-22 15:57
Valuations on Division Rings, we define valuations and describe the associated structures familiar from commutative valuation theory: the valuation ring ., its unique maximal left and maximal right ideal?., the residue division algebra?., and the value group Γ.. We also describe an important and distinctively noncommutative fea作者: LATER 時間: 2025-3-22 18:06
Graded Algebra,equire information that is specific to graded modules. We collect in this chapter the basic definitions and results on graded algebras and modules that will be of constant use in subsequent chapters. In §. we define graded rings, modules, and the gradings on their homomorphism groups and tensor prod作者: cortex 時間: 2025-3-23 00:27
Value Functions,ld associated graded structures that are graded vector spaces and graded algebras. We emphasize value functions whose associated graded structures have good properties: those called . on vector spaces and . on algebras. The use of gauges is a key aspect of our approach to valuation theory on divisio作者: 細(xì)胞膜 時間: 2025-3-23 01:53 作者: 阻塞 時間: 2025-3-23 06:00
Graded and Valued Field Extensions,valued field is an enhanced version of the residue field, inasmuch as it encapsulates information about the value group in addition to the residue field. It thus captures much of the structure of the field, particularly in the Henselian case. This point is made clear in §., where we show that—when t作者: 褲子 時間: 2025-3-23 13:36
Brauer Groups,ain analogues of the general results on the Brauer group of fields. Graded fields have a special structure however, since the degree?0 component is a canonically-defined subfield. This structure is reflected in a canonical filtration of the Brauer group of graded fields. The second section aims to r作者: 不能妥協(xié) 時間: 2025-3-23 14:47 作者: Lament 時間: 2025-3-23 19:58
Division Algebras over Henselian Fields,ng results for graded division algebras, then lifting back from . to .. This is facilitated by results in §. on existence and uniqueness of lifts of tame subalgebras from . to .. In §., we describe four fundamental canonical (up to conjugacy) subalgebras of . that reflect its valuative structure. Th作者: Habituate 時間: 2025-3-23 22:57 作者: Autobiography 時間: 2025-3-24 05:17
Indecomposable Division Algebras,e give examples of indecomposable algebras, emphasizing constructions that use valuation theory. In light of the primary decomposition, we restrict attention to division algebras of prime power degree. Indecomposable algebras of exponent?.. or higher are relatively easy to construct as “.-th roots” 作者: Brochure 時間: 2025-3-24 09:00
Computation of ,,(,),. This group? ..(.) is a subtle invariant of .. that has been of longstanding interest to those working with central simple algebras, algebraic groups, and .-theory. Since .. is a Brauer class invariant, it suffices to compute .. for division algebras. We prove here nearly all the known formulas for作者: A精確的 時間: 2025-3-24 12:59
The Essential Dimension of Central Simple Algebras,eters needed to define it. For a prime number ., the essential .-dimension is a variation of essential dimension that takes into account simplifications in structure that can occur after field extensions of degree prime to .. In §. we define the basic notions of essential dimension and essential .-d作者: Explicate 時間: 2025-3-24 15:46
Book 2015search over the last forty years. Its development was spurred in the last decades of the twentieth century by important advances such as Amitsur‘s construction of non crossed products and Platonov‘s solution of the Tannaka-Artin problem..This study is particularly timely because it approaches the su作者: Ingredient 時間: 2025-3-24 23:05 作者: 反省 時間: 2025-3-25 00:54
Computation of ,,(,), ..(.) for . a tame central division algebra over a Henselian field. We do this by first obtaining in §. formulas for .. in the graded setting, where calculations are substantially easier and more transparent. We then recover in §. the corresponding formulas in the valued setting by proving in Th.?. that . for .=.(.) Henselian and . tame over ..作者: 極小 時間: 2025-3-25 07:20
Jean-Pierre Tignol,Adrian R. Wadsworthd the power of this algebraic scheme, but the subject only began to be appreciated more widely after the publication of Chevalley‘s book, ‘The Algebraic Theory 978-94-010-8602-8978-94-009-4728-3Series ISSN 1389-2185 作者: 倫理學(xué) 時間: 2025-3-25 07:59 作者: 思考 時間: 2025-3-25 13:48 作者: 神秘 時間: 2025-3-25 15:54 作者: 去才蔑視 時間: 2025-3-25 20:42
Brauer Groups,aded field. This result is fundamental for the use of graded algebras to study division algebras over Henselian fields. An application is given to obtain a split exact sequence for the inertially split part of the Brauer group of a Henselian field. Another application of the theorem yields Witt’s de作者: membrane 時間: 2025-3-26 01:35
Total Ramification, graded field (i.e., .. is separably closed), we prove a group isomorphism from .(.) to the part of . of torsion prime to . mapping ., where . is the canonical pairing induced by commutators. For . not inertially closed, this leads to a description of .(.)/..(.) as a subgroup of . determined by the 作者: 雪崩 時間: 2025-3-26 05:01
Division Algebras over Henselian Fields,. is inertially split and . is tame and totally ramified over .. We show further that every inertially split division algebra . is Brauer equivalent to some .?.., where . is inertial over . and . is decomposably semiramified. The classes . for the . appearing in the .?.. decompositions of . are show作者: Anthrp 時間: 2025-3-26 09:30
Indecomposable Division Algebras,elds examples of exponent?2 and degree?8 in ?§., and of exponent?.≠2 and degree .. with .≥2 in §.. The last section, §., deals with complete decompositions into tensor products of symbol algebras. The main result is Th.?., which relates armatures in an inertially split division algebra over a Hensel作者: Fortuitous 時間: 2025-3-26 14:12
The Essential Dimension of Central Simple Algebras,hen in §. we sketch their method to obtain lower bounds on the essential .-dimension of central simple algebras. In the final §., we discuss consequences of these lower bounds for the decomposability of division algebras into tensor products of symbol algebras.作者: Libido 時間: 2025-3-26 17:45
Book 2015ecomposable algebras. In addition, the use of valuation theory in reduced Whitehead group calculations (after Hazrat and Wadsworth) and in essential dimension computations (after Baek and Merkurjev) is showcased..The intended audience consists of graduate students and research mathematicians..作者: arsenal 時間: 2025-3-26 21:16
Jean-Pierre Tignol,Adrian R. Wadsworth provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.978-90-277-2561-5978-94-009-6292-7Series ISSN 0168-1222 Series E-ISSN 2365-6425 作者: 我要威脅 時間: 2025-3-27 03:07 作者: 憲法沒有 時間: 2025-3-27 07:56 作者: 慢慢沖刷 時間: 2025-3-27 13:06 作者: demote 時間: 2025-3-27 15:05
Jean-Pierre Tignol,Adrian R. Wadsworthlently, . . and . . belong to the . in complex spacetime, respectively. The space coordinates of . . and . . give the spatial orientations and radii of the dishes, while their time coordinates determine the . of the emission and reception processes. The .(y) of the communication process is a convex 作者: Pessary 時間: 2025-3-27 21:01
Jean-Pierre Tignol,Adrian R. Wadsworthetric, bilinear form . such that .(x, x) = .(x). The choice of . fixes the contraction .?. in ?. and permits the introduction of a Clifford product x. = x?. x?. of x ∈ . and . ∈ ? .. This gives rise to the Clifford algebra of the symmetric bilinear form 1/2(.(x,y)+.(y,x)) when the characteristic ≠ 2作者: 平息 時間: 2025-3-28 00:43
Jean-Pierre Tignol,Adrian R. Wadsworthy vulnerable to climate change impacts; it is affecting us all, but the impacts are uneven (Field et al. 2014), requiring different kinds of transformative learning processes in different places and contexts. In this chapter, we therefore propose that, under climate change conditions, we view learni作者: 旁觀者 時間: 2025-3-28 03:40
Value Functions on Simple Algebras, and Associated Graded Rings作者: 反應(yīng) 時間: 2025-3-28 06:24
Springer Monographs in Mathematicshttp://image.papertrans.cn/v/image/980350.jpg作者: Ataxia 時間: 2025-3-28 11:25
https://doi.org/10.1007/978-3-319-16360-4Associated Graded Algebra; Brauer Group; Division Algebra; Ramification; Valuation作者: Admonish 時間: 2025-3-28 16:21
Jean-Pierre Tignol,Adrian R. WadsworthProvides the first comprehensive treatment of valuation theory for finite-dimensional division algebras.Showcases an innovative new approach to valuation theory via associated graded structures.Includ作者: vasculitis 時間: 2025-3-28 21:45 作者: 指數(shù) 時間: 2025-3-29 02:42
Value Functions on Simple Algebras, and Associated Graded Rings978-3-319-16360-4Series ISSN 1439-7382 Series E-ISSN 2196-9922 作者: 小卷發(fā) 時間: 2025-3-29 06:36 作者: 古老 時間: 2025-3-29 09:44
Jean-Pierre Tignol,Adrian R. Wadsworth vector space over GF(2) = *#x007B;0, 1*#x007D; which comes equipped with a quadratic form . and associated alternating bilinear form .. Properties of the finite geometry over GF(2) of ... — in part familiar, in part less so — are given a rather full description, and a dictionary of translation into作者: 偽善 時間: 2025-3-29 15:16
Jean-Pierre Tignol,Adrian R. Wadswortheralisation to n-dimensional space of quaternions, which Hamilton used to represent scalars and vectors in real three-space: it is also a development of Grassmann‘s algebra, incorporating in the fundamental relations inner products defined in terms of the metric of the space. It is a strange fact th作者: 公豬 時間: 2025-3-29 19:22 作者: frozen-shoulder 時間: 2025-3-29 21:23 作者: 提名 時間: 2025-3-30 02:28 作者: 苦澀 時間: 2025-3-30 05:50
